- "Author's reasons behind criticism of Bayesian Network"
- "Relation between Bayesian Networks and Causal Diagrams"
- "From objectivity to subjectivity"

Outside References
- "Helpful article about Bayesian Networks"
- "Reference for"How Bayesian Networks work""

Specific Nodes that were Helpful for Learning Bayesian Networks

- before discussing Bayesian networks, Pearl discusses the history and significance, using examples to further explain the concepts, of Bayes' rule and inverse probability from pages 95 - 108
- Pearl then connected this concept to Bayesian networks by discussing belief propagation from pages 108 - 112
- references past sections: "Although Bayes didn't know it, his rule for inverse probability represents the simplest Bayesian network. We have seen this network in several guises now: Tea -> Scones, Disease -> Test, or, more generally, Hypothesis -> Evidence" (Pearl, 2018, p. 112)
- explains the junctions present in both Bayesian networks and causal diagrams, using examples, from pages 113-116
- from pages 117 - 122, Pearl discusses conditional probability tables in relation to Bayesian networks and also mentions inverse-probability (previously discussed starting pages 97-99)
- from pages 122 - 133, Pearl discusses Bayesian networks in various contexts
- for the rest of the chapter (pages 128 - 133), Pearl compares Bayesian networks and causal diagrams

Explanations from "The Book of Why" about Bayesian Networks

University of Michigan - Ann Arbor

Examples of Collaboratively Learning Data Science on 1Cademy

Here is an example of how the collaboration between students, over the last semester, helped the class learn difficult concepts, which were not clearly explained in two of the required textbooks of the course: An Introduction to Statistical Learning (ISL) and The Book of Why (TBW):
We started with ISL, where we learned regression analysis and dimensionality reduction methods like PCA, shrinkage, step-wise, ... Then, we continued with TBW that clearly explains how to identify "confounders," "colliders," and "mediators," but very superficially explains how to deconfound a confounder. 

Initially, a student created a node that states, based on TBW, that in regression models, one should control for confounders. But TBW doesn’t say how to control for confounders.

So a different student linked that node to a node that previously been created, based on material in the ISL textbook. That linked node explains how to control for an independent variable in a regression model.

Two other students took the idea that we should not include "colliders" and "mediators" in our regression models that they learned from TBW and drew links between this reasoning and the cluster of dimensionality reduction methods taken from ISL. They explained that the dimensionality reduction methods only make sense for the purpose of prediction and classification where we care about improving the prediction accuracy. For causal inference, these methods fail and we should employ causal diagrams and the procedures explained in TBW to identify "confounders," "colliders," and "mediators;" and only include confounders, but never "colliders" or "mediators," in our regression model.

Later on, other students further completed these explanations and links, based on TBW, by reasoning for why common methods that are usually advised by statisticians and economists to "control for as many variables as possible" and "use dimensionality reduction methods" fail in causal inference, as they may open back-door paths and introduce new confounders in our analysis.

Collaboratively Learning Deconfounding in Causal Inference on 1Cademy

In addition to the content from the two textbooks, students found outside references, and summarized the essence of what they learned with their peers on 1Cademy to clarify and expand on what the community learned from the course textbooks:

S1 found interest in studying the paper "Path Diagram for technology use on self-directed learning, student engagement and academic performance" that used a causal diagram for inferring the Average Causal Effect (ACE) of self-directed learning, technology use, and student engagement on academic performance. 

Using the nodes from ISLR (such as linear regression), and nodes from The Book of Why (such as mediator, collider, etc. ) the S1 helped their peers synthesize the material of two different sources to gain an understanding of how to interpret the content of the research paper with ease. This way, whenever a student had difficulty understanding one of the nodes summarized from this paper, they were able to look at its parent nodes and quickly study the prerequisite concepts.

Students found outside references, and summarized the essence of what they learned with their peers on 1Cademy

- Elijah: S1
- Victoria: S2
- Medha: S3
- Xinhao: S4
- Zeyao: S5
- Yuko OR  (41.902496337891, -87.67259979248): S6
- Shahbab: S7
- Charlie: S8
NO S9
- Miles: S10
- Amar: S11
- Corlaban: S12
- Sulyman: S13
- Madeline: S14
- Iain: S15
- 42.30679, -83.705902: S16
- Hamza: S17
- Erica: S18
NO S19
- Hojoon: S20
- Wenfei: S21
- Sean: S22
- Ellen: S23
- Gurpreet: S24

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